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Existence and approximation of solutions of second-order nonlinear four point boundary value problems

โœ Scribed by Rahmat Ali Khan; Rosana Rodriguez Lopez

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
207 KB
Volume
63
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

We study some four point boundary value problems. We use the method of upper and lower solutions to improve some previous existence results, and apply the generalized method of quasilinearization to obtain a monotone sequence of iterates converging uniformly and rapidly to a solution of the problem.

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โœ Ruyun Ma; Nelson Castaneda ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 97 KB

We study the existence of positive solutions to the boundary-value problem u + a t f u = 0 tโˆˆ 0 1 i=1 a i < 1, and m-2 i=1 b i < 1. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem in cones.